Classical Hamiltonian Dynamics and Lie Group Algebras

TL;DR

This paper explores how classical Hamiltonian dynamics can be used to describe systems with Lie group symmetries, including examples like magnetic moments and non-abelian chromodynamics.

Contribution

It demonstrates that Hamiltonian equations can model a wide range of physical systems with Lie group symmetries using elementary algebraic methods.

Findings

Hamiltonian structure handles various differential equations.

Models magnetic moment precession and non-abelian chromodynamics.

Uses elementary algebraic methods for symmetry description.

Abstract

The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure to describe many physical systems exhibiting Lie group symmetries. Elementary examples include magnetic moment precession and the mechanical orbits of color charged particles in classical non-abelian chromodynamics.